Ron, I know you like making up words, but if you're going to ask someone to show you something, it's common courtesy to stick to words that are actually defined.

Provide the word that I made up here martimusÃ¢â‚¬Â¦ And, please provide said evidence to substantiate the fallacious accusation you just made.

Once you rephrase your question about "an arithmetic, a mathematic, or a geometry" accordingly, I'll get back to you.

The question is correctly stated as per the context martimus. It has not yet been answered.

With all due respect [or maybe not],

Again with the Ã¢â‚¬Å“Argumentum ad HominemÃ¢â‚¬Â due to a lack of refutation martimusÃ¢â‚¬Â¦

it's a grade school concept to say that numbers have to be represented physically.

ItÃ¢â‚¬â„¢s not grade school martimus, its fact. You probably should address that fact instead of skirting it.

Given that you perpetuate such claims, it really doesn't seem too likely that you've had much math. But by all means, feel free to prove me wrong: have you ever taken abstract algebra or real analysis?

Your spurious attacks to cover for a lack of refutation isnÃ¢â‚¬â„¢t working martimus.

Arithmetic is in essence completely abstract (its very basis [a pun?Ã‚Â maybe..] lies, more or less, in abstract algebra)!Ã‚Â I mean, if you define the natural numbers via the set-theoretic definition (http://en.wikipedia....natural_numbers) so that 0={}, 1={0}, 2={0,1} and so on, and if you then define addition by the definition with cardinalities of the corresponding sets of the added numbers, then in order to say something as simple as 2+2, you need to say that the union of {0,1} and {2,3} (ensuring that the sets are disjoint) is {0,1,2,3}, which is the definition of 4, and so 2+2=4.Ã‚Â Math is essentially a complete abstraction, something completely based on arbitrarily defined axioms (after all, why shouldn't we define addition to correspond to be the cardinality of the intersection of sets as opposed to the union?), but it remains something that can be conclusively, non-empirically, proved based on those axioms.

Yes, but when you assign values to it it ceases to be abstract. For exampe, x=s(X) y=s(Y) so |x|+|y|=s(xUy)(the addition rule as I remember it). Find the union of two given disjoint sets is not abstract. At least from what I remember, and addition, at least, at least as Ron would conisder it would be the latter.

BTW dude, you're actually familiar with set theory and abstract algebra at 18??? I'm impressed. I didn't know a union or intersection were anything other than a group of workers and a place where two road meet at that age. Personally I hated abstract algebra(algebra structures where I went to college). That class was the single reason I blew off my math minor. Are you familiar with analysis as well???

Yes, but when you assign values to it it ceases to be abstract.Ã‚Â For exampe, x=s(X) y=s(Y) so |x|+|y|=s(xUy)(the addition rule as I remember it).Ã‚Â Find the union of two given disjoint sets is not abstract.Ã‚Â At least from what I remember, and addition, at least, at least as Ron would conisder it would be the latter.

I suppose it depends on how you want to define 'abstract' in this sense. I still don't have a clue what Ron means when he's talking about showing him a mathematic or an arithmetic, but I figure that for these purposes it's adequately abstract when you don't define something like 2+2 in terms of counting some thing -- which as far as I can tell is what Ron's going on about. That is, 2+2=4 isn't at all empirical, since you can prove it without resorting to experiment where you just enumerate things (i.e. it follows naturally from axioms -- you don't conclude that 2+2=4 by putting two sets of two apples together and seeing what you get).

BTW dude, you're actually familiar with set theory and abstract algebra at 18???Ã‚Â I'm impressed.Ã‚Â I didn't know a union or intersection were anything other than a group of workers and a place where two road meet at that age.Ã‚Â Personally I hated abstract algebra(algebra structures where I went to college).Ã‚Â That class was the single reason I blew off my math minor.Ã‚Â Are you familiar with analysis as well???

I've always been about 5 years ahead when it comes to math -- at this point I've more or less got a complete undergrad math education down. But I hate algebra too -- groups are fine and all, but rings and fields and field extensions and irreducible polynomials and quotient fields and quotient rings and Galois fields -- it's all intolerable beyond that.

I'm familiar with analysis, but only on the real line -- I'll be taking a more topology-based analysis sequence next year.

Just what is "a mathematic," "an arithmetic", or "a geometry"? You're asking a nonsensical question.

It is no more nonsensical then the argument you are attempting to make martimus. Especially when you back your argument with ad Hominem attacks instead of sound logic. Because, we are, in fact, arguing logic, rationality and the metaphysical versus the physical in relation to empiricism here, and not mathematics. Mathematics is nothing more than the medium (or vehicle) of example in this dialogue martimus.

The laws of mathematics are metaphysical (just like a thought, love, the Laws of Logic, etcetera), the application of mathematics are not. When you apply (or evidence) the laws of mathematics physically (via speech, writing, oranges, fingers or toes) you make mathematics empirical via physical actuation. In this way you can either validate or invalidate your hypothesis. BUT, until you physically validate your hypothesis, said hypothesis is not empirical.

Now, when you physically say 2+2=4, you have actualized said hypothesis. But when you just think 2+2=4 you have actualized nothing because it is still metaphysical (i.e. Ã¢â‚¬Å“abstractÃ¢â‚¬Â). The problem youÃ¢â‚¬â„¢re running into is my choice of saying 2+2=4. We all know 2+2=4 is an empirical fact martimus, I choose to use the simple math equation as an example because it cannot be denied, but is still a fine (yet simple) example. A headier equation is not needed when a simple one will do. So your arguments and ad Hominem attacks are a Non sequitur within the context of this discussion.

No, I would imagine the answer as eight. To say it would require the physical action of actually speaking the words.Which, once again proves the point you are attempting to deny.

No the action of you speaking is your means of sharing the information, not the means to how you came to the conclusion. The act of you coming to the conclusion was based on no physical visual medium. Don't twist the words around in an attempt to benefit yourself.

The laws of mathematics are metaphysical (just like a thought, love, the Laws of Logic, etcetera), the application of mathematics are not.

Ron, thoughts, love, laws of logic are not metaphysical. They are constructs created from biological interactions between hormones and chemicals released by the brain. There is nothing mysterious and metaphysical about them, even if we don't know the full interactions between said chemcials and hormones. Take for instance a schizophrenic who hears voices in his head. Now you would probably say that he/she is possessed or controlled by sin to such a degree to hear voices. But in actuallity it is more likely a syncing problem with the individuals internal monologue (time is not controlled by just one portion of the brain, but by many portions of the brain); which is a near constant for everyone who has a working brain. There is no metaphysical about it. The same goes with mathematics, they are based on proofs rather than physical evidence, and need no physical evidence to be proven.

The laws of mathematics are metaphysical (just like a thought, love, the Laws of Logic, etcetera), the application of mathematics are not. When you apply (or evidence) the laws of mathematics physically (via speech, writing, oranges, fingers or toes) you make mathematics empirical via physical actuation. In this way you can either validate or invalidate your hypothesis. BUT, until you physically validate your hypothesis, said hypothesis is not empirical.

If you think that maths relies on physical actuation and physical validation, could you please show me a five dimensional cube? Could you calculate its volume and then physically show me its volume?

If you think that maths relies on physical actuation and physical validation,

Absolutely, and you have as-of-yet to invalidate my assertion; or that of the inductive evidences of empirical validation over the history (through antiquity) of rationality. But you, in the same breath, proved my assertion by coalescing your thoughts into physicality by verbalizing them. There again, your thoughts have not been proven valid though, they have only been given physicality.

And empirical mathematics works the same way (as I have described numerous times in this post). Until you provide physicality for it, it remains metaphysical. And they cannot be proven empirical until they have been validated by physical experimentation.

could you please show me a five dimensional cube?

Be more specific and describe the five dimensions you want this cube in, and weÃ¢â‚¬â„¢ll see if we can give verification to it.

Could you calculate its volume and then physically show me its volume?

If you can provide physical validation for said cube, and it is within the scope of our physical measuring devices; then yes we can physically show its volume. If not, then no; we cannot physically show its volume.

No the action of you speaking is your means of sharing the information, not the means to how you came to the conclusion.

I never said it did, therefore you are either; misunderstanding what I said, un-intentionally misquoting what I said, or purposefully twisting what I said

You may want to go back and re-read the thread to understand the context of the conversation.

The act of you coming to the conclusion was based on no physical visual medium. Don't twist the words around in an attempt to benefit yourself.

Once again, you are either; misunderstanding what I said, un-intentionally misquoting what I said, or purposefully twisting what I said.

But you are also incorrect in your assertion. I came to my conclusion by the physical visual medium of either; 1- physically counting objects, 2- physically writing out an equation, 3- physically reading the conclusions of others

THEN: conducting experimentation via the empirical scientific method of induction (repeated experimentation in a controlled environment) to either validate or disprove the models I had along the way.

Ron, thoughts, love, laws of logic are not metaphysical.

Show me a picture of a red logic. Show me a picture of a green love. Show me a picture of a purple thought.

They are constructs created from biological interactions between hormones and chemicals released by the brain. There is nothing mysterious and metaphysical about them, even if we don't know the full interactions between said chemcials and hormones. Take for instance a schizophrenic who hears voices in his head. Now you would probably say that he/she is possessed or controlled by sin to such a degree to hear voices. But in actuallity it is more likely a syncing problem with the individuals internal monologue (time is not controlled by just one portion of the brain, but by many portions of the brain); which is a near constant for everyone who has a working brain. There is no metaphysical about it. The same goes with mathematics, they are based on proofs rather than physical evidence, and need no physical evidence to be proven.

You have just spouted a series of opinions and attempted to promulgate them as empirical facts.

Again: Show me a picture of a red logic. Show me a picture of a green love. Show me a picture of a purple thought.

But you are also incorrect in your assertion. I came to my ocnclusion by the physical visual medium of either;1- physically counting objects,2- physically writing out an equation,3- physcially reading the conclusions of others

So you came to the conclusion by physically counting imagined objects, or did you actually count physical objects to find out what 4+4 equals? If imagined is it then a physical medium? Do a schizophrenics visual hallucinations then actually exist? No. You more than likely instantly knew what 4+4 equals thru repetition and physical application during the learning process as a child. You didn't even need to imagine what the answer was, because it was precisely a reflexive act without the existence of any physical visual medium.

THEN: conducting experimentation via the empirical scientific method of induction (repeated experimentation in a controlled environment) to either validate of disprove the models I had along the way.

Once again a relexive act. There was no experimentation for the conclusion of 4+4.

Show me a picture of a red logic.Show me a picture of a green love.Show me a picture of a purple thought.

First off, intangible emotions and thoughts cannot consist of a color nor of shape, unless you have Synesthesia. Now instead of letting these statements irritate me I'll entertain them, but first I'll introduce the problems with the statements in the form of questions.

Does the red logic then not exist to a blind man?Does the green love then not exist to a monochromatic?Does the purple thought then not exist to a tetrachromatic?

Now, on to the pictures:

Green love. More commonly known as the Caudate nucleus, which is interestingly also the epicenter for common problems with obsession and various other behavioural problems.

Red logic and purple thought contained in same picture because they both occur in the frontal lobes.

You have just spouted a series of opinions and attempted to promulgate them as emperical facts.

Yes I have, as a form of informing you that these things are being found to be of purely biological function. One of my hobbies is researching the brain; mostly because I'm trying to write the most biologically accurate way a zombie apocalypse could occur. That's here nor there, but a common misconception is that everyone percieves time the same, which is false. Everyone percieves time differently and this is a purely biological function. One thing I've stumbled across is how the brain handles time. Comes to find out that research is showing time seems to slow down during life threatening events. This is because the amount of information you begin to take in during life threatenings events is enormous compared to the information of non-life threatening events, and this time dilation occurs because of problems with the information being relayed between the differet parts of the brain while simultaneously having the brain attempt to recalibrate the time respective to the information in order to predict the stage of events about to occur; something that happens second after second even while you read this. Now remember, it may seem that time is slowing down, but it's not, you're just remembering it that way. Now this realization caused a group of scientists to research the auditory hallucinations of schizophrenics; their hypothesis being that dysfunction in the time syncing of the brain causes the schizophrenic to imagine a voice in their head. So far the results are supporting their hypothesis. So I ask you, what were you saying?

I suppose it depends on how you want to define 'abstract' in this sense.Ã‚Â I still don't have a clue what Ron means when he's talking about showing him a mathematic or an arithmetic, but I figure that for these purposes it's adequately abstract when you don't define something like 2+2 in terms of counting some thing -- which as far as I can tell is what Ron's going on about.Ã‚Â That is, 2+2=4 isn't at all empirical, since you can prove it without resorting to experiment where you just enumerate things (i.e. it follows naturally from axioms -- you don't conclude that 2+2=4 by putting two sets of two apples together and seeing what you get).

I never actually thought of empirical and abstract being opposites. Empirical date is gained through experimentation and observation which we've all been saying in this thread.

I've always been about 5 years ahead when it comes to math -- at this point I've more or less got a complete undergrad math education down.Ã‚Â But I hate algebra too -- groups are fine and all, but rings and fields and field extensions and irreducible polynomials and quotient fields and quotient rings and Galois fields -- it's all intolerable beyond that.

I'm familiar with analysis, but only on the real line -- I'll be taking a more topology-based analysis sequence next year.

Cool, about all I've been able to retain is up to PDE and some numerical analysis. You're 18 and you know more math than anyone in this thread. You should feel proud.

Be more specific and describe the five dimensions you want this cube in, and weÃ¢â‚¬â„¢ll see if we can give verification to it.

A hypercube of side length 2 resting in 5 dimensional Euclidean space. I've completely specified the question to the extent that any competent mathematician would be able to do it -- now you solve it your way and I'll do it mine.

A hypercube of side length 2 resting in 5 dimensional Euclidean space.Ã‚Â

As I said:

If you can provide physical validation for said cube, and it is within the scope of our physical measuring devices; then yes we can physically show its volume. If not, then no; we cannot physically show its volume.

As of your last post you have failed to do so.

I've completely specified the question to the extent that any competent mathematician would be able to do it --

Actually, you have failed to address my answer to your post. And your fallacious ad Hominem attack on competency not withstanding, I would desire you to stick to the context of the conversation, and quit side stepping it with red herring's and straw men tangents.

now you solve it your way and I'll do it mine.

The resolution to your hypothetical hypothesis simply proves that until you empirically/physically prove your model, it remains a model...